Answer:
(u o w) (7) = 22
(w o u) 7) = 8
Step-by-step explanation:
We are given:
[tex]u(x)= x^2+6\\w(x)= \sqrt{x+9}[/tex]
We need to find:
a) (u o w) (7)
First we will find (u o w) (x) and then we will find (u o w) (7)
We know that (u o w) (x) = u(w(x))
Put value of w(x) into u(x)
we have:
[tex]u(x)=x^2+6\\Put\: x =\sqrt{x+9}\\u(w(x))=(\sqrt{x+9})^2+6\\u(w(x))=x+9+6\\ u(w(x))=x+15[/tex]
Now finding (u o w) (7)
We know that: (u o w) (7) = u(w(7))
[tex]u(w(x))=x+15\\Put\:x=7\\u(w(7))=7+15\\u(w(7))=22[/tex]
So, (u o w) (7) = 22
b) (w o u) (7)
First we will find (w o u) (x) and then we will find (w o u) (7)
We know that (w o u) (x) = w(u(x))
Put value of u(x) into w(x)
we have:
[tex]w(x)= \sqrt{x+9}\\Put\:x=x^2+6\\w(u(x))= \sqrt{(x^2+6)+9}\\w(u(x))= \sqrt{x^2+6+9}\\w(u(x))= \sqrt{x^2+15}[/tex]
Now finding (w o u) (7)
We know that (w o u) (7) = w(u(7))
[tex]w(u(x))= \sqrt{x^2+15}\\Put\:x=7\\w(u(7))= \sqrt{(7)^2+15}\\w(u(7))= \sqrt{49+15}\\w(u(7))= \sqrt{64}\\w(u(7))= 8[/tex]
So, (w o u) (7) = 8
